The present invention relates to a new and distinct strawberry cultivar designated ‘DrisStrawThree’ and botanically known as Fragaria×ananassa. This new strawberry cultivar was discovered in October, 2002 and originated from a cross between the female parent ‘5F205’, a proprietary strawberry plant (unpatented) and the male parent ‘San Juan’ (U.S. Plant Pat. No. 12,899). The original seedling of the new cultivar was asexually propagated at a nursery in Shasta County, Calif. ‘DrisStrawThree’ was subsequently asexually propagated and underwent further testing at a nursery in Ventura County, Calif. for four years. The present invention has been found to retain its distinctive characteristics through successive asexual propagations.